XYl NOTATIONS

Yx, ^(X,Y) set of mappings of X into Y: 1.4

lx identity mapping of X: 1.4

x-*T(x) mapping: 1.4

F(A) direct image: 1.5

F~1(A) inverse image: 1.5

F"1^) inverse image of a one element set {y}: 1.5

F(. , y\ F(x9 .) partial mappings of a mapping F of A c X x Y into

Z: 1,5

/A natural injection: 1.6

F"1 inverse mapping of a bijective mapping: 1.6

G ° F composed mapping: 1.7

O;I);UL family: 1.8

N set of natural integers: 1.8

{xl9..., xn} set of elements of a finite sequence: 1.8

(J AA, (J AA union of a family of sets: 1.8

AeL A

P) AAJ p) AA intersection of a family of sets: 1.8

XeL *.

X/R quotient set of a set X by an equivalence relation R:

1.8

Yl XA product of a family of sets: 1.8

AeL

prj projection on a partial product: 1.8

(WA) mapping into a product of sets: 1.8

R set of real numbers: 2.1

x + y sum of real numbers: 2.1

xy product of real numbers: 2.1

0 element of R: 2.1

—x opposite of a real number: 2.1

1 element of R: 2.1
jc""1, l/x inverse in R: 2.1
x^~y,y^x order relation in R: 2.1
x <y, y> x relation in R: 2.1
]a,A[, [a,b], [a,b[9 ]a,b] intervals in R: 2.1

R+, Rj set of real numbers ^0 (resp. >0): 2.2

\x\9 x+, x" absolute value, positive and negative part of a real

number: 2.2

Q set of rational numbers: 2.2

Z set of positive or negative integers: 2.2

l.u.b. X, sup X least upper bound of a set: 2.3

g.l.b. X, inf X greatest lower bound of a set: 2.3

sup f(x)9 inf f(x) supremum and infimum of/in A: 2.3

x € A xeA

R extended real line: 3.3f the plane. 4. Simple arcs and simple closed curves.ess to unpublished lecture notes and manuscripts,